BioMedical Admissions Test (BMAT) Practice Test 2026 - Free BMAT Practice Questions and Study Guide

To calculate the volume of a cone or pyramid, you use the formula that involves one-third of the product of the base area and the height. The reasoning behind this is rooted in geometry, as both cones and pyramids can be conceptualized as a form of a prism or a cylinder with a pointed or tapered end.

In both cases, the volume is derived from the idea that the base area is an important determinant of the space the shape occupies, and the height provides the necessary dimension to extend that base area vertically. The factor of one-third accounts for the fact that these shapes are relatively less voluminous than a cylinder or prism of the same base area and height. Over our understanding of geometry, it has been determined that when a cone or pyramid is filled with solid material, it occupies only one-third of the volume that a corresponding prism or cylinder would occupy when both have the same base area and height.

This formula is pivotal in applications ranging from architecture to materials science, as it provides a practical means for determining how much of a substance can fit into a cone or pyramid-shaped container. Thus, the expression "1/3 area × height" precisely captures this relationship.